Analysis of trigonometric implicit Runge-Kutta methods

Title:	Analysis of trigonometric implicit Runge-Kutta methods
Authors:	Hoang Si Nguyen Roger B. Sidje Nguyen Huu Cong
Keywords:	oscillatory ODEs variable stepsize variable coefficients trigonometric collocation implicit RK
Issue Date:	2007
Publisher:	ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Citation:	ISIKNOWLEDGE
Abstract:	Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods.
Description:	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 198 Issue: 1 Pages: 187-207 Published: JAN 1 2007 ; TNS07658
URI:	http://www.sciencedirect.com/science/article/pii/S0377042705007867 http://repository.vnu.edu.vn/handle/VNU_123/31873
ISSN:	0377-0427
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science